Enhanced secondary motion of the turbulent flow through a porous square duct

Authors: Samanta, A.S., Vinuesa, R., Lashgari, I., Schlatter, P., Brandt, L.B.
Document Type: Article
Pubstate: Published
Journal: Journal of Fluid Mechanics
Volume: 784   681-693
Year: 2015


Direct numerical simulations of the fully developed turbulent flow through a porous square duct are performed to study the effect of the permeable wall on the secondary cross-stream flow. The volume-averaged Navier-Stokes (VANS) equations are used to describe the flow in the porous phase, a packed bed with porosity epsilon = 0.95. The porous square duct is computed at Reb = 5, 000 and compared with the numerical simulations of a turbulent duct with four solid walls. The two boundary layers on the top wall and porous interface merge close to the center of the duct, as opposed to the channel, because the side wall boundary layers inhibit the growth of the shear layer over the porous interface. The most relevant feature in the porous duct is the enhanced magnitude of the secondary flow, which exceeds that of a regular duct by a factor of 4. This is related to the increased vertical velocity, and the different interaction between the ejections from the side walls and the porous medium. We also report a significant decrease in the streamwise turbulence intensity over the porous wall of the duct (which is also observed in a porous channel), and the appearance of short spanwise rollers in the buffer layer, replacing the streaky structures of wall-bounded turbulence. These spanwise rollers most likely result from a Kelvin–Helmholtz type of instability, and their width is limited by the presence of the side walls.